Can't add custom activity

Can't say I understand your dev/debugging environment if you have to hand-retype the request.

In any case your payload doesn't conform at all to the docs, which show:

{
   "input" : [
      {
         "leadId" : 1001,
         "activityDate" : "2013-09-26T06:56:35+07:00",
         "activityTypeId" : 1001,
         "primaryAttributeValue" : "Game Giveaway",
         "attributes" : [
            {
               "name" : "URL",
               "value" : "http://www.nvidia.com/game-giveaway"
            }
         ]
      }
   ]
}

attributes is an array of objects. Each object has two own properties, name and value.  You're doing something very different, and obvs. that's why it's breaking.